1. Field of the Invention
The present invention relates generally to the field of interferometric fiber optic gyroscopes (IFOGs), and more particularly, to a method for measuring an intensity-type polarization non-reciprocity (PNR) bias error in an IFOG.
2. Description of Related Art
As discussed in U.S. Pat. No. 4,881,817, herein incorporated by reference, a fiber optic gyroscope typically comprises a single loop of optical fiber, which has a pair of light waves coupled to travel in opposite directions around the loop. If the loop is rotated, the counter-propagating light waves experience a phase-shift due to the well-known Sagnac effect. By detecting a phase difference between the two light waves caused by the Sagnac effect, the rotation rate of the loop can be determined.
FIG. 1 is a graph illustrating how the Sagnac effect can be used to determine the rotation rate of a fiber loop. An interferometer is used to measure a phase difference+between the counter-propagating waves. The observable output power is given by the following equation: EQU P=P.sub.o /2(1+cos .phi.)
where P.sub.o is the nominal input power. If the phase difference .phi. is zero, then P=P.sub.o, and the loop is stationary. However, as the loop is rotated, the Sagnac effect causes the phase to shift by .OMEGA.. Notice, that at .phi.=.OMEGA., the value of P is only slightly less than P.sub.o. Thus, measuring the phase shift around P=P.sub.o is difficult.
One technique used to overcome this problem recognizes that at .phi.=+/-.pi./2, the slopes of the cosine function are at a maximum and are of opposite sign. If the light waves are modulated with a square wave signal having a period of .tau. microseconds, where r is the time it takes the light waves to travel around the loop, the phase of the output signal can be shifted to +/-.pi./2. If the loop is also rotating, an additional phase shift is present, which causes the phase shift to be slightly greater than .pi./2 in one direction (point a.sub.2), and slightly less than .pi./2 in the other direction (point a.sub.1). The phase shift component caused by rotation can be determined by measuring the difference between the minimum a.sub.1 and maximum a.sub.2 output power levels, denoted by A in FIGS. 1 and 2.
FIG. 2 is a graph of the output power versus time. If the loop is not rotating, and no other effects are considered, the output power resulting from the square wave modulation would be a constant P.sub.o /2 (line 200). As a result of the rotation, however, the output is a square wave (line 202), having an amplitude A. This signal is then demodulated using a photodetector to calculate the amplitude A. This amplitude value A is proportional to the phase shift .OMEGA.. The phase shift is likewise proportional to the rotation rate. Thus, the rotation rate of a fiber loop can be determined.
If the optical path lengths around the loop are equal for both counter-propagating waves, the interferometer is said to be "reciprocal." However, in practice, most fiber interferometers are not reciprocal, due to imperfections in optical fibers. Most commercially available optical fibers are birefringent (i.e. doubly refractive), resulting in two different orthogonal polarization modes, each mode propagating light at a different velocity. In addition, birefringence of the optical fibers is sensitive to environmental factors such as temperature, pressure, strain, etc. Thus, practical interferometers are known as being "non-reciprocal," since birefringence causes counter-propagating waves to travel different optical path lengths around the loop, resulting in a phase difference between the waves, even if the loop is at rest. One type of error induced by the difference in polarization between the two paths is known as intensity-type polarization non-reciprocity (PNR) bias error.
The birefringence-induced phase difference (PNR bias error) is a major source of error in fiber optic gyroscopes. In fact, the error can be on the same order of magnitude as the Sagnac effect itself, or even larger. Moreover, the PNR bias error is not constant over time, and is therefore difficult to actually eliminate. One solution to reduce the PNR bias error is to use special polarizing fiber to reduce coupling between the polarization modes. During the manufacturing process, the special polarizing fiber is subjected to mechanical stresses to increase the birefringence of the fiber. This reduces coupling between the modes, since the high birefringence tends to preserve the polarization of the light waves. However, even using the special polarization-preserving fiber, the PNR bias error is still a factor.
U.S. Pat. No. 4,881,817, noted above, teaches a device for minimizing PNR bias error in a fiber optic gyroscope. Essentially, the device forces the PNR error to occur all the time by using a relatively fast modulation. If the error is known to occur, it can be averaged out over time and effectively eliminated. However, this disclosure does not teach any method or device for actually measuring the amount of PNR bias error present in a particular fiber optic loop. A method for measuring the PNR bias error present in a fiber optic loop is needed for use in manufacturing environments, where certain physical parameters may be adjusted to minimize the error while the loop is still in assembly.
One known technique for measuring PNR bias error is to vary the temperature of the loop, and measure the resulting PNR bias error. Since the birefringence cross-coupling is temperature dependent, the loop can be placed into an industrial oven, and the PNR bias error measured for different temperatures. If the results over the measured temperature range (typically 50.degree. C.-150.degree. C.) are unacceptable, the loop may be rejected or corrective action taken. This process takes several hours, however, and is difficult to use on an assembly line.
Thus, there is a need for a method which can accurately determine the amount of intensity-type PNR bias error in a relatively short period of time, without heating and/or cooling the fiber optic loop.